Day 0/28Hinds mated 0Contests 0FPS 0

Drag to orbit · wheel / pinch to zoom · labels: stag number, mass and fat share · stags roar to attract hinds and to warn rivals

Red Deer Rut Lab: Roaring Contests, Harem Defence and the Fat Budget of a Stag

Autumn in a Highland glen. Stags roar, size each other up, and the winners hold harems of hinds for a few weeks without eating much. Change the stags and the rules, run the season, and see who mates and who burns out.

Educational model. A simplified daily model of a rut: roaring is an honest signal of fighting ability, contests are decided by who gives up last, and energy comes from fat. Wounds are shown only as a small loss of strength. Numbers are typical order-of-magnitude values, not data from one real herd.

Scenario

The herd and the rules

Follow / inspect stag

Stags

Fat reserve through the rut (% of body mass)

Hinds in each harem

Contest log

Experiment 1: does the bigger stag win?

Runs 20,000 contests for each size ratio between two stags in equal condition. The war-of-attrition formula predicts P(bigger wins) = r^γ / (1 + r^γ), where r is the strength ratio and γ is how sharply rivals read each other.

Experiment 2: 40 seasons

Repeats the rut 40 times with the herd settings above and reports the average number of matings for the heaviest, second heaviest, ... stag at the start, the inequality of matings (Gini) and the average mass lost.

Independent numerical checks

Also run in Node: node src/check.js.

Controls

Drag or one finger: orbit; wheel or pinch: zoom. Views: Overview, Follow stag, Contest (jumps to the current contest).
Next day plays one day; Run to end finishes the season instantly; New season restarts with the same seed (change the seed for a different herd).
The stag table updates every day; the green and red rows mark harem holders and exhausted stags.

The science

Roaring is an honest signal. Red deer stags roar at a rate (roars per minute) that follows their condition: R = 12 · rhp in the model, clipped to 1.5–22. The rate cannot be faked cheaply because roaring costs energy and fatigue, so hinds and rivals can use it to judge a stag (Clutton-Brock & Albon 1979, as a classic field study).

Resource-holding potential. rhp = (M/160 kg) · (0.5 + 0.5 F/F₀) · (1 − wound): heavier and fatter stags are stronger; a small wound factor lowers it after hard contests.

War of attrition. Two stags escalate through roaring, parallel walking and, rarely, antler contact. Each has a mean persistence m = 25 min · rhp^γ and quits at a random exponential time. Then P(A wins) = m_A/(m_A + m_B) = r^γ/(1 + r^γ) with r = rhp_A/rhp_B, and the contest lasts m_A m_B/(m_A + m_B) minutes on average. Both pay the cost of the time the loser lasted: 8, 12 or 40 kcal/min in the roaring, walking and antler phase [model values].

Energy. Basal rate BMR = 70 M^0.75 kcal/day (Kleiber). A rutting stag spends (2.0 + 0.08 R + 0.6 if holding a harem) times BMR and eats only 0.35 BMR (half of that when guarding hinds) [model values]. Fat of 9,400 kcal/kg is burned: dM/dt = −k M^0.75, which has the exact solution M^0.25 = M₀^0.25 − 0.25 k t; the page checks the simulation against it. A 150 kg stag loses about 18 % of its mass in 28 days; field studies report stags losing up to a fifth of their body mass.

Hinds. Each hind is in oestrus (receptive) for one day, about a Gaussian around mid-season with a spread of 0.18 of the season [model]. Hinds drift towards stags roaring at the highest rates (weight R⁵). A hind in oestrus mates with her harem holder 92 % of the time; about 10 % of matings are taken by a roaming stag [model].

Simplifications and honest limits. One-day steps; no age, no antler size effect, no hind choice beyond roar rate, no sneaker strategy beyond a fixed rate, no calves, no weather. The 3D scene shows the outcome of the daily model; stags and hinds walk with rigid leg swings. Outcomes of single seasons are random: use the 40-season experiment for averages.